Complete question :
Let X be a random variable with the following probability distribution: Find the standard deviation of X.
X :____ - 2 ___ 3 ____ 5
P(x) __ 0.3 __ 0.2 ___ 0.5
Answer:
3.04
Explanation:
Given the data :
X :____ - 2 ___ 3 ____ 5
P(x) __ 0.3 __ 0.2 ___ 0.5
σ = √(Σ(x - μ)²*p(x))
μ = E = Σ(x*p(x)) = (-2*0.3) + (3*0.2) + (5*0.5) = 2.5
σ = √ ((-2 - 2.5)^2 * 0.3) + ((3 - 2.5)^2 * 0.2) + ((5 - 2.5)^2 * 0.5)
σ = √9.25
σ = 3.04138
σ = 3.04